UV map and re texturing it
Don't feel bad about understanding all of this, it can be very confusing and it takes a while to get.

There are a lot of bases to hit here, and they are all deep enough to be a full paying job in their own right.  Hopefully, this info should help you ask more targeted questions with this info, so here we go:

UV Maps are just a way of relating 2D information (like a picture) to a 3d object (such as a model). 
  
Blender can generate these for you by going into edit mode, selecting everything (a), and pressing u for the unwrap menu, and choosing "smart unwrap" (results are sub-optimal, but "good enough").  Unwrapping models are an art to themselves, because where cuts are added to the model to allow the UV's to be made flat can be noticeable.  

Once you have a UV map, textures can be applied to your model.  The simplest one is Diffuse, as this the model's color (the rainbow example pictured above).  There are other maps that you may use that will affect how those colors are shown further, depending on renderer and shader, such as Gloss, Emission, Specular, or even Transparency (to name only a few).

A Normal Map is an extremely special kind of texture.  This is a way to fake geometric detail into a model that doesn't have the geometry itself to pull it off.  Someone usually does this in order to preserve detail from a high poly sculpt while still being able to use the model in a game or animate with.


You will usually know you are dealing with a Normal Map (sometimes referred to as a Tangent Map) if it is mostly purple with fluorescent reds and greens here and there.  



The usual way to generate a Normal Map is to take a high-poly model and bake on the details to a lower detailed model, Blender is capable of doing this.  There are also programs that let you draw directly on Normal maps, but as far as I know, Blender is not one of them.